The dependencies are fine. Things haven't blown up here.

I did a targeted rsync, which was actually MUCH faster than I was expecting. I rebooted, and palemoon crapped out with exactly the same error.
It's a permissions thing. So I ran X logged in as root, and sure enough, Palemoon worked. Bah! So, to narrow it down, I made a luser on the sdcard, and THAT luser ran Palemoon on the sdcard. That clears the palemoon package. So it's permissions thing peculiar to my SSD. That sends me away growling and muttering to look after my own install.

Is there any debug option on these type of browsers for startup errors?

maybe the rights change during the transfer, try

OK - Sorted.

I have some funny things in /etc. One was that I got fed up with browsers building up massive sized caches, so I developed a handy dodge. I made the ~/.cache/ directories symlinks to directories in /dev/shm, which vanish every reboot. Somewhere along the line, (perhaps at the update?) I lost my modified /etc/rc.d/rc.local which made the directories in /dev/shm with user permissions. I did have a /dev/shm/moonchild\ productions/ directory there,so my symlink in ~/cache looked good. But it was root:root so I couldn't write to it, hence my error. I don't reboot this thing often

Chromium or Firefox didn't mind, but Palemoon did. The theme error still exists, I think but I'm writing this as a user on my RazPi in Palemoon-32.3.0 which I think says it all. The only hangup is that I have a /dev/shm/BraveSoftware for Brave, and Brave of course isn't here. Who cares? I'll twiddle that now.